Membrane transfer coefficient

The membrane transfer coefficient is a function of (1) the diffusion coefficient in the phase occupying membrane pores and (2) various membrane geometric parameters. Assuming pure Fickian diffusion in a symmetric microporous membrane, can be shown as [5]... 

Each term on the right side of Equation 4.2 represents an individual resistance. Hollow-fiber diameters are Henry coefficient (liquid-gas equilibrium constant) for the species in question. With liquid-liquid contact, the term H in Equation 4.2 should be replaced by OTd, the equilibrium distribution coefficient between the tube-side liquid and the shell-side liquid. The membrane transfer coefficient is a function of (1) the diffusion coefficient in the phase occupying membrane pores and (2) the various geometric parameters of the membrane. Assuming pure Eickian... 

The model is based on an engineering approach and requires knowledge of modeling constants such as resistance of membrane, transfer coefficient, etc. The main assumptions of the model are as follows ... 

The larger sucrose molecule partitions into the pore and diffuses more slowly through water and encounters a higher drag from the pore walls, resulting in 3.27 times lower membrane transfer coefficient. 

The transport of solute from the feed through the membrane to the receiving solution may be influenced by the solute transport resistance in the feed liquid and the permeate liquid. In the absence of pore convection, the value of the membrane transfer coefficient will be given by expressions (3.4.95c) and (3.4.96b). Referring to Figure 3.4.8, the solute flux at steady state can be expressed as... 

Correlations for the mass-transfer coefficient, as the Sherwood number for various membrane geometries have been reviewed (39). 

Equation (20-80) requires a mass transfer coefficient k to calculate Cu, and a relation between protein concentration and osmotic pressure. Pure water flux obtained from a plot of flux versus pressure is used to calculate membrane resistance (t ically small). The LMH/psi slope is referred to as the NWP (normal water permeability). The membrane plus fouling resistances are determined after removing the reversible polarization layer through a buffer flush. To illustrate the components of the osmotic flux model. Fig. 20-63 shows flux versus TMP curves corresponding to just the membrane in buffer (Rfouimg = 0, = 0),... 

A phenomenon that is particularly important in the design of reverse osmosis units is that of concentration polarization. This occurs on the feed-side (concentrated side) of the reverse osmosis membrane. Because the solute cannot permeate through the membrane, the concentration of the solute in the liquid adjacent to the surface of the membrane is greater than that in the bulk of the fluid. This difference causes mass transfer of solute by diffusion from the membrane surface back to the bulk liquid. The rate of diffusion back into the bulk fluid depends on the mass transfer coefficient for the boundary layer on feed-side. Concentration polarization is the ratio of the solute concentration at the membrane surface to the solute concentration in the bulk stream. Concentration polarization causes the flux of solvent to decrease since the osmotic pressure increases as the boundary layer concentration increases and the overall driving force (AP - An) decreases. 

The flux rate is obtained from the slope of the receptor chamber solute concentration versus time plot. The mass transfer coefficient, hh is equal to PA, where A is the surface area of the membrane separating the two subcompartments. 

The membrane and diffusion-media modeling equations apply to the same variables in the same phase in the catalyst layer. The rate of evaporation or condensation, eq 39, relates the water concentration in the gas and liquid phases. For the water content and chemical potential in the membrane, various approaches can be used, as discussed in section 4.2. If liquid water exists, a supersaturated isotherm can be used, or the liquid pressure can be assumed to be either continuous or related through a mass-transfer coefficient. If there is only water vapor, an isotherm is used. To relate the reactant and product concentrations, potentials, and currents in the phases within the catalyst layer, kinetic expressions (eqs 12 and 13) are used along with zero values for the divergence of the total current (eq 27). 

The reverse osmosis membranes were tested in the standard experimental set-up (10). The experiments were carried out at three different pressures 17.4, 40.8 and 102 bars the corresponding sodium chloride concentrations were 3500 ppm, 5000 ppm and 29000 ppm. Before the reverse osmosis runs, membranes were thermally shrunk for 10 minutes in water and subsequently pressurized at 15-20% higher pressures than those used during the reverse osmosis experiments. A feed flow rate of 400 ml/mln was used giving a mass transfer coefficient k = 40 x 10 cm/s on the high pressure side of the membrane. 

It should be obvious from the above that fluid-management techniques which Improve the mass-transfer coefficient (k) with minimum power consumption are most desirable. However, in some cases, low-cost membrane configurations with inefficient fluid management may be more cost effective. In any case, it is important to understand quantitatively how tangential velocity and mem-brane/hardware geometry affects the mass-transfer coefficient. 

The mass and heat transfer analogies make possible an evaluation of the mass-transfer coefficient (k) and provide insight into how membrane geometry and fluid-flow conditions can be specified to optimize flux (4). For laminar flow ... 

Plate and frame systems offer a great deal of flexibility in obtaining smaller channel dimensions. Equations 4 and 5 show that the Increased hydrodynamic shear associated with relatively thin channels Improves the mass-transfer coefficient. Membrane replacement costs are low but the labor involved is high. For the most-part, plate and frame systems have been troublesome in high-pressure reverse osmosis applications due to the propensity to leak. The most successful plate and frame unit from a commercial standpoint is that manufactured by The Danish Sugar Corporation Ltd. (DDS) (Figure 15). 

The basic membrane/hardware geometries-tubes, plate and frame, and hollow fibers can of course all be operated with fluid management techniques which are relatively efficient or non-efficient. The remainder of this paper will adress itself to novel fluid-management techniques which utilize the basic membrane/hardware geometries but which seek to augment the mass-transfer coefficient even further. 

Considerable interest has been generated in turbulence promoters for both RO and UF. Equations 4 and 5 show considerable improvements in the mass-transfer coefficient when operating UF in turbulent flow. Of course the penalty in pressure drop incurred in a turbulent flow system is much higher than in laminar flow. Another way to increase the mass-transfer is by introducing turbulence promoters in laminar flow. This procedure is practiced extensively in enhanced heat-exchanger design and is now exploited in membrane hardware design. 

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